(Intercept) x
1 1 1.920595
2 1 3.093363
3 1 5.301387
4 1 8.990286
5 1 1.218501
6 1 8.882287
Find me: Manchester 342
“truth … is much too complicated to allow anything but approximations”
- John von Neumann
John von Neumann, wearer of funny hats via https://farkasdilemma.wordpress.com/2013/01/04/john-von-neumannm-wearer-of-funny-hats/
“All models are wrong, but some are useful”
- George Box
DavidMCEddy at en.wikipedia CC BY-SA 3.0 , via Wikimedia Commons
\[y = \beta_0 + \beta_1 x + \varepsilon\]
Where is \(\beta_0\)
Where is \(\beta_0\)
Where is \(\beta_1\)
Where is \(\beta_1\)
\[y = \beta_0 + \beta_1 x + \varepsilon\]
\[ X = \begin{bmatrix}1 & x_1\\ \vdots & \vdots \\ 1 & x_n\end{bmatrix},\quad \beta = \begin{bmatrix}\beta_0\\ \beta_1\end{bmatrix} \]
(Intercept) x
1 1 1.920595
2 1 3.093363
3 1 5.301387
4 1 8.990286
5 1 1.218501
6 1 8.882287
\[y = \beta_0 + \sum_{j=1}^{J} \beta_j B_j(x) + \varepsilon\]
(Intercept) ns(x, df = 3)1 ns(x, df = 3)2 ns(x, df = 3)3
1 1 -0.095842465 0.4743374 -0.3103069
2 1 0.006273703 0.5498909 -0.3597333
3 1 0.444366108 0.4236598 -0.2337245
4 1 0.133806217 0.3714757 0.4916902
5 1 -0.103895176 0.3825795 -0.2502798
6 1 0.164715184 0.3660870 0.4649746
\[y = \sum_{k=1}^{K} \beta_k \, \mathbf{1}\{x \in R_k\} + \varepsilon\]
ind1 ind2 ind3 ind4 ind5 ind6 ind7 ind8
1 0 0 0 0 0 0 0 1
2 0 0 0 0 0 0 1 0
3 0 0 0 0 0 0 1 0
4 0 0 0 0 0 0 0 1
5 0 1 0 0 0 0 0 0
6 0 0 1 0 0 0 0 0